Answer:
A. 6.9
Step-by-step explanation:
Edge 2020
The standard deviation for the set of population data given in the question is 6.9
How to determine the meanData = 14, 23, 31, 29, 33Number of data (n) = 5Summation of data = 14 + 23 + 31 + 29 + 33 = 130Mean (μ) =?Mean = summation of data / number
μ = 130 / 5
μ = 26
How to determine the standard deviationData = 14, 23, 31, 29, 33Mean (μ) = 26Number of data (n) = 5Standard deviation (σ) =?σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)²] / n]
σ = √[[(14 - 26)² + (23 - 26)² + (31 - 26)² + (29 - 26)² + (33 - 26)²] / 5]
σ = √[236 / 5}
σ = 6.9
Learn more about statistics:
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A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is true. Let p ˆ be the proportion in a sample of 100 such ABC batteries. What is the probability that this sample proportion is within 0.05 of the population proportion.
Answer:
78.88% probability that this sample proportion is within 0.05 of the population proportion
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this question:
[tex]p = 0.8, n = 100[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
What is the probability that this sample proportion is within 0.05 of the population proportion.
This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.
X = 0.85
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944.
X = 0.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a pvalue of 0.1056.
0.8944 - 0.1056 = 0.7888
78.88% probability that this sample proportion is within 0.05 of the population proportion
In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
What is the area of the triangle?
PLSSS help me
Answer:
The area of the triangle is [tex]A=6 \:units^2[/tex].
Step-by-step explanation:
The area A of a triangle is given by the formula [tex]A=\frac{1}{2} bh[/tex] where b is the base and h is the height of the triangle.
From the graph, we can see that the base is 3 units and the height is 4 units. Therefore, the area of the triangle is
[tex]A=\frac{1}{2} \cdot3\cdot 4=\frac{12}{2}=6 \:units^2[/tex]
Employees that work at a fish store must measure the level of nitrites in the water each day. Nitrite levels should remain lower than 5 ppm as to not harm the fish. The nitrite level varies according to a distribution that is approximately normal with a mean of 3 ppm. The probability that the nitrite level is less than 2 ppm is 0.0918.
1. Which of the following is closest to the probability that on a randomly selected day the nitrite level will be at least 5 ppm?
(A) 0.0039
(B) 0.0266
(C) 0.0918
(D) 0.7519
(E) 0.9961
Answer: .0039
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to find the inverse of f(x) = y = 3x / 8 + x
Answer:
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the function
[tex]f(x) = \frac{3 x}{8+x}[/tex]
Given function is one-one and onto function
Hence f(x) is bijection function
[tex]y = f(x) = \frac{3 x}{8+x}[/tex]
now cross multiplication, we get
( 8+x)y = 3 x
8 y + x y = 3 x
8 y = 3 x - x y
taking Common 'x' we get
x (3 - y) = 8 y
[tex]x = \frac{8 y}{3-y}[/tex]
Step(ii):-
The inverse function
[tex]x = \frac{8 y}{3-y} = f^{l}(y)[/tex]
The inverse function of x
[tex]f^{l}(x) = \frac{8 x}{3-x}[/tex]
Final answer:-
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?
Answer:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 = \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]
We have the following data given:
[tex]n_1 =20[/tex] represent the sample size for group 1
[tex]n_2 =20[/tex] represent the sample size for group 2
[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1
[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2
[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1
[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]
And the deviation would be just the square root of the variance:
[tex]S_p=3.678[/tex]
The statistic is givne by:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference, that is:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]
What is the mean and the standard error of the distribution of differences?For each sample, we have that they are given by
[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]
[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]
Hence, for the distribution of differences, the mean and the standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{3.3 - 0}{1.163}[/tex]
[tex]t = 2.84[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].
Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
More can be learned about the t-distribution at https://brainly.com/question/16313918
will mark the branliest to first one who answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
Need help with this math problem
Answer:
[tex]f(x)=-5x-3[/tex].
Step-by-step explanation:
From the given machine diagram it is clear that:
[tex]f(x)=-8[/tex] at [tex]x=1[/tex]
[tex]f(x)=-13[/tex] at [tex]x=2[/tex]
[tex]f(x)=-18[/tex] at [tex]x=3[/tex]
It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.
Since the function changing at a constant rate, therefore it represents a linear function.
If a linear function passing through two points, then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is
[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]
[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]
[tex]y+8=-5(x-1)[/tex]
[tex]y=-5x+5-8[/tex]
[tex]y=-5x-3[/tex]
So, the required function is [tex]f(x)=-5x-3[/tex].
9x-3=87 what is the anwser
Answer:
x=10
Step-by-step explanation:
9x-3=87
add 3 to both sides
9x=90
divide by 9 on both sides
x=10
Answer:
x=10
Step-by-step explanation:
9x-3=87
you add 3 to both sides
9x-3(+3)=87(+3)
which equals
9x=90
90/9= 10
answer:
x =10
I hope this helped!
A slot machine has 3 dials each dial has 30 positions one of which is jackpot. To win jackpot all three dials must be in jackpot position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot
Answer:
3/90
Step-by-step explanation:
1 slot is 1/30
2 slot is 1/30
3 slot is 1/30
this gives you that 3/90 when you had them
Answer:
D) 1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Step-by-step explanation:
Find two numbers for which the sum is 101 and the difference is 47
Answer:
74 and 27
Step-by-step explanation:
let x and y be the numbers
x + y =101........eqn 1
x - y = 47.......eqn 2
solve simultaneously
from equation 2, make x the subject
x= 47 + y........eqn 3
put eqn 3 into eqn 1
(47+y) + y = 101
47 + 2y = 101
2y= 101 - 47
2y=54
y= 54/2
y= 27
put y=27 into eqn 3
x = 47 + 27
x = 74
Graph the circle (x-3)^2+(y-7)^2=4
Brittany Monroe is a legal secretary. Her biweekly salary is $1,650.00 what is her annual salary?
Answer:
$42,900 a year
Step-by-step explanation:
so there are 26 bi-weeks in a year. (fun fact)
you take $1,650 and multiply that biweekly to get her annual salary.
1650*26=42,900
Which fraction is in simplest form 4/20 6/9 5/13 14/21
Answer: 5/13
Step-by-step explanation:
Answer:
5/13 is in simplest form, because it cannot be reduced any further.
Step-by-step explanation: 4/20 can be reduced to 1/5, 6/9 to 1/3, and 14/21 can be reduced to 2/3
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answer:
⅓ m/s
Step-by-step explanation:
Area of a square is:
A = s²
Take derivative of both sides with respect to time:
dA/dt = 2s ds/dt
Given that dA/dt = 6 m²/s and s = 9 m:
6 m²/s = 2 (9 m) ds/dt
ds/dt = ⅓ m/s
The Formula of the area of a square: A = bh or A = s^2
Solution:
~Take derivative of both sides
da/dt = 2s * ds/dt
~Use given values (6m^2/s and 9m)
6 = 2(9) * ds/dt
~Simplify
1/3m/s = ds/dt
Best of Luck!
3(12−5)+(8x8)-45? Answer?
Answer:
its 40
Step-by-step explanation:
i think
10 X 5/11=
just multiplication get it right and get brainlyest
60pts or whatever it narrows it down to
The answer is 4.55
When you divide 5 by 11 you will get 0.45454545454 than when you multiply these numbers by 10 you will get 4.54545454545 and then the rounded answer is 4.55.
Answer: 4.54
Step-by-step explanation:
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
B because first you need to read the problem and understand the information.
A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.
Answer:
D. Observational Study
Explanation:
An observational study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.
This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study is subject to bias because a positive or negative result might be because of other factors not related to the study.
Sally wants to fill ten 8-inch tea glasses. How much tea does she need?
A) 80 ounces
B) 40 ounces
C) 80 cubic inches
D) Not enough information to answer
Answer
I believe C considering cubic mass
Answer:
D
Step-by-step explanation:
Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??
Answer: [tex]3(3-4x+2y)[/tex]
Step-by-step explanation:
[tex]9-12x+6y[/tex]
[tex]3(3-4x+2y)[/tex]
what is the cube root of 1
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above
Answer:
The problem is clearly solved in the attachment
Junior bought a bag of mixed fruit snacks. The flavors in the bag are 4 strawberry, 3 cherry, and 5 grape. If he chooses one fruit snack at random, what it the probability of the first one being grape?
Answer:I believe it would be 5/12
Step-by-step explanation:
You add all of them up then since it's 5 grapes and in total there is 12 fruit snacks. It should be 5 grapes of 12 fruit snacks in the bag.
e is 5 more than d.
fis 7 less than d.
a) Write an expression for e in terms of d.
Answer:
C
Step-by-step explanation:
Answer:
e = d + 5
Step-by-step explanation:
e = d + 5
f = d - 7
Solve for e means write as e = ...d
and this is already there...
You can not write it more compact then this.
If you try, you will notice you finally end with the initial equation which you started with, or you endup with something which is obviously very true like
e = e or d = d.
What is the volume of this cube with a side length of 6 centimeters
6 cm
Answer:
V = 216 cm^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = (6)^3
V = 216 cm^3
Answer:216 cm^3
Step-by-step explanation:
In cube, the length of all sides are equal
length of side=6cm
Volume of cube=length x length x length
Volume of cube=6 x 6 x 6
Volume of cube=216
Volume of cube=216 cm^3
Which value has an absolute deviation of 5 from the mean of this data set?
26, 12, 35, 28, 14
A 28
B. 35
C. 26
D. 14
Answer: 28
Step-by-step explanation: see prev. explanation
The absolute deviation of 5 from the mean of this data set is 28.
What is absolute deviation?
Absolute deviation is "the distance between each data point to the mean".
According to the question,
The data set is 26, 12, 35, 28, 14
Average of the data set = [tex]\frac{sum of the data value }{Total number of observation}[/tex]
= [tex]\frac{26+12+35+28+14}{5}[/tex]
= [tex]\frac{115}{5}[/tex]
= 23.
Thus, the average of the data set is 23.
In order to find absolute deviation of 5 subtract each data point from the mean.
26 - 23 = |3| = 3
12 - 23 = |-11| = 11
35 - 23 = |12| = 12
28 - 23 = |5| = 5
14 - 23 = |-9| = 9.
Hence, the absolute deviation of 5 is from the mean of the data set is 28.
Learn more about absolute deviation here
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A fraction that is equivalent to 6/-5?
Answer:
12/-10
Step-by-step explanation:
Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.
Answer:
12/-10
Step-by-step explanation:
6/-5
6×2= 12
-5×2=-10
12/-10
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )
Answer:
[tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.
For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.
_____
Many calculators, spreadsheets, and web sites can do this tedious math for you.